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The connection between mathematics and
art goes back thousands of years. Mathematics has been
used in the design of Gothic cathedrals, Rose windows,
oriental rugs, mosaics and tilings. Geometric forms were
fundamental to the cubists and many abstract expressionists,
and award-winning sculptors have used topology as the
basis for their pieces. Dutch artist M.C. Escher represented
infinity, Möbius bands, tessellations, deformations,
reflections, Platonic solids, spirals, symmetry, and
the hyperbolic plane in his works.

Mathematicians and artists continue to
create stunning works in all media and to explore the
visualization of mathematics--origami, computer-generated
landscapes, tesselations, fractals, anamorphic art, and
more.

One uncut square of paper, 8" by 8" by 8", 2009. This piece uses intersecting pleats to create tension within the folded sheet and encourage three-dimensionality. In addition to sharp points created by stretching pleats close to the four corners of the original sheet, it also features a joint where the centers of two opposite sides of the square are held together by a folded lock mechanism, creating the appearance of a non-simply connected surface. "I fold (mostly flat and mostly paper) surfaces into interesting shapes. To do this, I use sequences of pleats to arrange layers so that they create tension that forces the material towards a curved surface. The simplest of these pieces are more appropriately described as discovered than created, but in others I build on the basic equilibrium shape to bend and curve the pleated surface further. The mathematics show up in many ways, but the two of my favorite are the combinatorics in the arrangement of pleats and the mathematical physics in understanding the forms preferred by the paper when folded." --- Goran Konjevod (Arizona State University, Tempe, and Livermore, CA) http://organicorigami.com